A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equati...A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 （2005） 94. The positive energy states of system are discussed and the conclusions are made properly.展开更多
The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI...The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI（R^n）, ｜·｜f ∈ L^2（R^n）}. When the nonlinearity is focusing and L2-supercritical, the authors give sufficient conditions for the solutions to blow up in finite time for both confining and repulsive potential. Especially for the repulsive case, the solution to the deterministic equation with the initial data satisfying the stochastic blow-up condition will also blow up in finite time. Thus, compared with the deterministic equation for the repulsive case, the blow-up condition is stronger on average, and depends on the regularity of the noise. If φ = 0, our results coincide with the ones for the deterministic equation.展开更多
We propose improved ring shaped like potential of the form,V（r,θ）=V（r）＋（h^2/2M r^2）[（βsin^2θ＋γcos^2θ＋2λ）/sinθcosθ]^2 and its exact solutions are presented via the Nikiforov–Uvarov method.The angle ...We propose improved ring shaped like potential of the form,V（r,θ）=V（r）＋（h^2/2M r^2）[（βsin^2θ＋γcos^2θ＋2λ）/sinθcosθ]^2 and its exact solutions are presented via the Nikiforov–Uvarov method.The angle dependent part V（θ）=（h^2/2M r^2）[（βsin^2θ＋γcos^2θ＋λ）/sinθcosθ]^2,which is reported for the first time embodied the novel angle dependent（NAD）potential and harmonic novel angle dependent potential（HNAD）as special cases.We discuss in detail the effects of the improved ring shaped like potential on the radial parts of the spherical harmonic and Coulomb potentials.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No. 60806047the Basic Research of Chongqing Education Committee under Grant No. KJ060813
文摘A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 （2005） 94. The positive energy states of system are discussed and the conclusions are made properly.
基金supported by the National Natural Science Foundation of China (Nos. 10871175,10931007,10901137)the Zhejiang Provincial Natural Science Foundation of China (No. Z6100217)the Specialized ResearchFund for the Doctoral Program of Higher Education (No. 20090101120005)
文摘The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI（R^n）, ｜·｜f ∈ L^2（R^n）}. When the nonlinearity is focusing and L2-supercritical, the authors give sufficient conditions for the solutions to blow up in finite time for both confining and repulsive potential. Especially for the repulsive case, the solution to the deterministic equation with the initial data satisfying the stochastic blow-up condition will also blow up in finite time. Thus, compared with the deterministic equation for the repulsive case, the blow-up condition is stronger on average, and depends on the regularity of the noise. If φ = 0, our results coincide with the ones for the deterministic equation.
文摘We propose improved ring shaped like potential of the form,V（r,θ）=V（r）＋（h^2/2M r^2）[（βsin^2θ＋γcos^2θ＋2λ）/sinθcosθ]^2 and its exact solutions are presented via the Nikiforov–Uvarov method.The angle dependent part V（θ）=（h^2/2M r^2）[（βsin^2θ＋γcos^2θ＋λ）/sinθcosθ]^2,which is reported for the first time embodied the novel angle dependent（NAD）potential and harmonic novel angle dependent potential（HNAD）as special cases.We discuss in detail the effects of the improved ring shaped like potential on the radial parts of the spherical harmonic and Coulomb potentials.
